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A 25 m tower standing vertically
A 25 m tower standing vertically on a hillside casts a shadow down the hillside that is 27 m long. The angle at the tip of the shadow S, subtended by the tower is 26...

Suppose you are at the gas station
Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation:
C(g)=3.03(g)
a) What does the number 3.03 represent?
b) Find C(2)
c) Find C(9)
d) For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose the number you did.
e) If you were to graph C(g), what would be an appropriate domain? ...

A ladder rests against a wall
A ladder rests against a wall. the top of the ladder reaches 15 feet up the wall, and makes an angle of 53 with the ...

A 10-ft ladder leans against a wall
A 10-ft ladder leans against a wall at an angle with the horizontal. The top of the ladder is x feet above the ground. If the bottom of the ladder is pushed toward the ...

An airplane is sighted at the same time
An airplane is sighted at the same time by two ground observers who are 4 miles apart and both directly west of the airplane. They report the angles of elevation as 11° and 22°...

A biologist is researching a newly-discovered species
A biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant "k" for the bacteria? (Round k to two decimal places.)

polynomial functions
Four boys are playing with their marbles. Two boys have the same number of marbles and they both have 1 more marble than the 3rd boy. The 4th boy has 1 marble less than the 3rd boy. If all the number of marbles of each boy is multiplied, the product would be 18...

A company produces a product
A company produces a product for $9.45 per unit, plus a fixed cost of $5200. The company sells the product for $15.80 per unit.
a) determine a function, c(x), to represent the cost production x units
b) determine a function, r(x) to represent the revenue from selling x units
c) determine a fucntion to represent profit
d) caculate break even point

A pig at Papas Barn just had a litter of piglets
A pig at Papas Barn just had a litter of piglets. The whole barn is about 12 miles long. In the middle of the night one piglet ran out of the barn a traveled down to the Bray Ranch which is about 13.5 miles away. When viewed on the towns map the two barns make a 115 degree ...

Beth owns her own candle making business
Beth owns her own candle making business. The cost to create and buy your own candle is $475. In addition to these one time charges, the cost of putting your own picture on the candle is $1.75. Let "x" equal the average cost per candle for Beth's business to ...

Julio works as a quality control expert in a beverage factory
Julio works as a quality control expert in a beverage factory. The assembly line that he monitors produces about 20,000 bottles in a 24-hour period. Julio samples about 120 bottles an hour and rejects the line if he finds more than 1/50 of the sample to be ...

A satellite, travelling in a circular orbit
A satellite, travelling in a circular orbit 700 km above Earth, will pass directly over a tracking station at noon. The satellite takes 95 mins to complete an orbit.
a) If the antenna for a tracking station is aimed at an angle of elevation of 30 degrees, at what time will the satelite pass through the beam of the ...

A new FDA diet claims that a person
A new FDA diet claims that a person weighing 140 pounds should consume 1560 daily calories and that a 180 pound person should consume 1700 ...

A rectangular shipping container
A rectangular shipping container has a volume of 2500 cm3. The container is 4 times as wide as it is deep, and 5cm taller than it is ...

A diver stands at the very end of a diving board
A diver stands at the very end of a diving board before beginning a dive. The deflecton (d) of the board at a position (s) feet from the stationary end is given by d=cs2(3L-s) for 0 is greater than or equal to s is greater than or equal to L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physica properties of the board. Suppose the board is 10 ft long.

a) If the deflection at the end of the board is 1 ft, find c
b) Show that the deflection is .5 foot somewhere between s=6.5 and s=6.6

From the top of a lighthouse
From the top of a lighthouse 160 feet above sea level, the angle of depression to a boat at sea is 25 degree. To the nearest ...

A crow is on the ground
A crow is on the ground 80 feet from the base of a 45 foot tall tree. It then flies straight through the air to the top of the ...

Two ships leave port at 4 p.m.
Two ships leave port at 4 p.m. One is headed at a bearing of N 38 E and is traveling at 11.5 miles per hour. The other is traveling 13 miles per hour at a bearing of S 47 E. How far apart are they when dinner is served at 6 p.m.?

Amelia sees a jet heading south away from her
Amelia sees a jet heading south away from her at 42 degree angle of elevation. Twenty seconds later the jet is still moving away from her, heading south at a 15 degree angle of elevation. If the jets elevation is constantly 6.3 ...

Mia has a temperature of 101 degrees
Mia has a temperature of 101 degrees. Her temperature is rising at the rate of 1 degree every 5 hours. If her temperature reaches 108 degrees, Mia's parents will take her to the emergency ...

Liselle is flying her kite
Liselle is flying her kite with 62 feet of string attached to the ground. She measures 5 feet of string from the ground to a point of 4 feet ...

A straight road makes an angle of 15 degrees
A straight road makes an angle of 15 degrees with the horizontal. When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the ...

A ferris wheel is built such that
A ferris wheel is built such that the height (h) in feet above the ground of a seat on the wheel at time (t) in sec can be modeled by: H(t)=53+50sin(π/10t-π/2)
Find the angular speed in radians and the linear speed in feet?

Due to wind, a tree grew
Due to wind, a tree grew so that it leaned 8 degrees from the vertical. From a point on the ground 28 meters from the base of the tree, the angle of elevation to the top of the tree is 24.6 ...

Coast Guard Station Able is located
Coast Guard Station Able is located 150 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able indicates that the ship is located N55°E; the call to Station Baker indicates that the ship is located S60°E.
(a) How far is each station from the ship?
(b) If a helicopter capable of flying 200 miles per hour is dispatched from the nearest station to the ...

Two observers,who are 2 miles apart
Two observers,who are 2 miles apart on a horizontal plane,observe a balloon the same vertical plane with themselves. The angles of elevation are 50' and 65' respectively. Find the height of the balloon ...

Greenshield`s Formula can be used
Greenshield's Formula can be used to determine the amount of time a traffic light at an intersection should remain green. G = 2.1n + 3.7 G= green time in seconds n = average number of vehicles traveling in each lane per light cycle. Write a simplified expression to represent the average green light time per vehicle

A tree on a hillside casts a shadow
A tree on a hillside casts a shadow 215 ft down the hill. If the angle of inclination of the hillside is 22 degrees to the horizontal and the angle of elevation of the sun is 52 ...

You need to determine the length
You need to determine the length of a tunnel drilled through a lunar peak at the center of a crater. From a point on the crater floor, you run ropes to the ends of the tunnel. The first rope's distance covered is 24.5 meters and the second rope's distance is 21.2 meters. The two ropes meet at an angle of 68 degrees.
a) What is the length of the ...

Three students in an outdoor pursuits program
Three students in an outdoor pursuits program collaborated to write an adventure travel guidebook for Alberta and BC. Two local publishers are interested in marketing and publishing it and both anticipate retailing the book for $20. Publisher "A" offers a straight royalty of 10% (on the retail price) on all book sales. Publisher "B" offers an 8% royalty for any books sold up to 5000 copies and will then increase the royalty to 15% for any copies sold in excess of 5000.

a) Describe the type of function
b) Find the functions A(x) and B(x) - notice that function A(x) is apiecewise defined function.
c) Let x be the number of books sold and let A(x) give the income under plan "A" and B(x) give the income under plan "B". Graph functions on the interval 0,10000

A ship at sea, the Admiral, spots two other ships
A ship at sea, the Admiral, spots two other ships, the Barstow and the Cauldrew and measures the angle
between them to be 65° . They radio the Barstow and by comparing known landmarks, the distance
between the Admiral and the Barstow is found to be 236 meters. The Barstow reports an angle of 36°
between the Admiral and the Cauldrew. To the nearest ...

The course for a bike race follows
The course for a bike race follows a triangular shaped trail. The first leg is a straight 6 kilometre ride. After that, the biker must turn 283 degrees to the left and follow the train to the next turn. Turning 269 degrees again to the left will take the biker to the finish line, which is exactly where he ...

In 1995, the number of families
In 1995, the number of families with cable television was 20.0 million. By the year 2008, there will be 27.6 families with cable television and enjoying every minute of ...

A straight road slopes upward
A straight road slopes upward at 15 degrees from the horizontal. How long is the section of the road that rises a vertical distance of 250 feet? ( Express the answer to the nearest 10 feet.)

The total sales for a new camera equipment store
The total sales for a new camera equipment store were 200,500 for the second year and 500,000 for the fourth year
a) find a linear equation for the above model
b) estimate the total sales for the 6th year

You are driving at a speed
You are driving at a speed of 55 miles per hour to your sisters house. At 1 pm, you are 150 miles from her ...

A pilot flies in a straight path
A pilot flies in a straight path for 1 hour and 30 minutes. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 hours in the new direction. If she maintatins a constant speed of 620 miles per ...

The cost of an ice cream sundae
The cost of an ice cream sundae is given by the formual C(s) = 1.25s + 5.00. In this formula, C(s) represents the cost of the ice cream sundae and s is the number of scoops of ice ...

To obtain a retail price, a dress shop
To obtain a retail price, a dress shop adds $20 to the wholesale cost of every dress. When the shop has a sale, every dress is sold for 75% of the retail price. Write functions f(x), g(x)...

A plane flies 1.3 hours at 110 miles per hour
A plane flies 1.3 hours at 110 miles per hour at a bearing or North 40 degrees East. It then turns and flies on a bearing of South 50 degrees East at the same rate for 1.5 hours. How far is the plane from the starting ...

Mary invested $1400 in two mutual funds
Mary invested $1400 in two mutual funds. One fund earned interest at 7% per year and the other earned interest at 8% per year. If she receives $104 in interest after one ...

Island A is 230 miles from island B
Island A is 230 miles from island B. A ship captain travels 270 miles from island A and then finds that he
is off course and 180 miles from island B. What angle, in degrees, must he turn through to head straight
for island ...

The linear equation y=30x describes
The linear equation y=30x describes how far from home Deena is as she drives from Dallas to Miama. Let x represent the number if hours and y represent the number of miles. How far from home Deena in 12 ...

Two observers 200 feet apart
Two observers 200 feet apart are in line with the base of flagpole. The measurement of the angle of elevation of the top from one observer is 30 degrees and other 60 ...

A mass suspended from a spring
A mass suspended from a spring is pulled down a distance of 2 feet from its rest position. The mass is released at time t=0 and allowed to oscillate. If the mass returns to this position after 1 ...

An airplane flying at an altitude of 6 miles
An airplane flying at an altitude of 6 miles, is on a flight path that goes directly over you. If angle is the angle of elevation, find the distance from the observer to plance at 30...

It costs $1.50 per day
It costs $1.50 per day to place a one-line ad in the classifieds plus a flat service fee. One day costs $3.50 and four days costs $8.00.

Write a linear equation in point slope form that gives the cost in dollars, y, in terms of the number of days the ad ...

In high school baseball, the front of the pitcher`s rubber
In high school baseball, the front of the pitcher's rubber is 60.5 feet away from the back end of the home plate, and the first base bag is 90 ft fromhome place. The home plate and each of the bases makes a 90 degree angle with the next one, and the pitcher's rubber is aligned between home place and second ...

An antenna is atop of a 80 foot building
An antenna is atop of a 80 foot building, 12 feet from the edge. From a point 60 feet from the base of the building, the angle from the ground level to the top of the building is 68 ...

Two firetowers are 30 kilometers apart
Two firetowers are 30 kilometers apart, tower A being due west of tower B. A fire is spotted from the towers and the bearings from A and B are E 14 degreesN and W 34 degreesN, ...

X and Y are two lighthouses
X and Y are two lighthouses, Y being 20 Km due east of X. From a ship due south of X, the bearing of Y was 055 degrees. Find the distance of the ship from ...

One afternoon your family goes out
One afternoon your family goes out to pick strawberries. At 1:00P.M., your family has picked 3 quarts. Your family finishes picking at 3:00P.M. and has 28 quarts of ...

From a point on the ground
From a point on the ground, a person notices a 110-foot antenna on the top of a hill subtends an angle of 1.5 deg. If the angle of elevation on the bottom of the antenna is 25 ...

You are driving from Grand Rapids, Michigan
You are driving from Grand Rapids, Michigan, to Detroit, Michigan. You leave Grand Rapids at 4:00 p.m. At 5:10 p.m. you pass through Lansing, Michigan, a distance of 65 miles. Write a linear equation that gives the distance in miles, d, in terms of time, t. Let t represent the number of minutes since 4:00 ...

Natali is 5 feet 3 inches tall
Natali is 5 feet 3 inches tall. She walks from the base of a broadcasting tower directly toward the tip of the shadow cast by the tower. When she is 130 feet from the tower and 3 feet from the tip of the tower's shadow, her shadow starts to appear beyond the tower's ...

Exponential Functions
anna needed to let everyone in the music club know the time of its next meeting. she called two people and asked each of them to call two other people, and so on. if each phone call takes one ...

Graphing Polynomial Functions
When there are 22 apple trees pre acre, the average yield has been found to be 500 apples per tree. For each additional tree planted per acre, the yield per tree decreases by 15 apples per ...

Exponential Functions
the period of a simple pendulum varies directly as the square root of its length. If a pendulum three feet long has a period of 4.8 ...

Exponential Functions
wendy, a loan officer at a bak has $1000000 to lend and is required to obtain an average return of 18% per year. if she can lend at the rate of 19% or at the rate of 16%...

Law Of Cosines
A flagpole 20ft. high was suited at the top of a hill. A string was tied from the top of the pole to the point P on the ground 150m. from the foot of the pole. If the flagpole measured an angle of 100 degree with the surface of the ...

Cosine
Three ships a b and c are anchored in the ocean. the distance from a to b is 25.5 km, from b to c is 17.2 km and from c to a is 37.4 ...

SOHCAHTOA
two towers a and b are located 48 m apart. Rod who is standing at the base of tower B found that the angle of elevation of tower a is twice the angle elevation of tower B as observed by Alexandra who is also standing at the base of tower \"A . At a point midway between their bases the angle elevation of two towers are complementary ...

SOHCAHTOA
From the top of a barn 25 feet tall, you see a cat on the ground. The angle of depression of the cat is 40 degrees. How many feet, to the nearest ...

Law Of Sines
A rocket tracking station has two telescopes A and B placed 1.1 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket ...

Exponential Functions
2. Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was $1.26 and in January 2006 the price of regular unleaded gasoline was $2.31 (Bureau of Labor Statistics, 2006). Use the coordinates (1997, 1.26) and (2006, 2...

Absolute Value Functions
Find the variation constant and an equation of variation where y veries directly as y and x=60 whenx=6

SOHCAHTOA
a yard stick, held vertically on a level surface, cast a show 1 foot 8 inches ...

Exponential Functions
the half life of radio-active cesium- 137 is 30.2 years. If we have 750 poiunds of radioactive ...

Exponential Functions
A bacteria culuture started with 8500 bacteria. In two hours, the number of bacteria had reached 9775. Find an expression for the number of bacteria t hours after it was first observed. Using your answer to (a), find the number of bacteria after 10 ...

Law Of Cosines
A flashlight was focused on the mirror forming an angle of 80 degrees. The length of the light from the flashlight to the mirror was 8 meters and the lengthof the reflected light to the wall was 7 ...

Law Of Sines
a pilot is flying over a straight highway. The angles of depression are 5 miles apart and are 32 degees and 48 ...

SOHCAHTOA
An advertising blimp hover over a stadium at an altitude of 125m. The pilot sights a tennis court at 8 degree angle of ...

Slope Intercept Form
pam has $25 and is earning $4 per week for doing chores. If she does not spend any ...

Composite Functions
Ron is saving money for college. Each month he deposits 10% of his net income plus an additional $50 into a savings account. His net income, after taxes have been taken out, is 80% of his gross income. a. Write a composite function for the amount that Ron saves each month if his gross income is g. b. Find the amount that Ron saves in a month when his gross income is $2400

Exponential Functions
crabon-14 decays at a rate of 11.4%every 1000 years.
a. write a formula for the quantity,Q, with an initial 200-gram sample as a function of time t, in years
b. How much of the 200 grams will remain after 1500 years

Law Of Cosines
Grandpa Violente wishes to find the distance between two points A and B on the opposite side of the river. On his side of the river he locates two trees that are 472 feet apart at C and D. He measures the angles w=17, x=66, y=59 and z=20, as ...

SOHCAHTOA
An advertising blimp hover over a stadium at an altitude of 125m. The pilot sights a tennis court at 8 degree angle of ...

Law Of Sines
A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 9 mi apart, to be 32° and 48°, as shown in the figure. Round your answers to the nearest tenth mile.

(a) Find the distance of the plane from point ...

Law Of Sines
AB is a line 652 feet long on one bank of a stream, and C is a point on the opposite bank. A = 58 degrees, and B = 48 degrees ...

Slope Intercept Form
a pool is being drained at a constant rate. the amount of water is a function of the number of minutes the pool has been draining, as shown in the table, write a equation in slpe intercept form that represents the function. then find the amount of water in the pool after two and a half hours

Law Of Sines
A tree growing on a hillside casts a 157ft shadow straight down the hill. Find the vertical height of the tree if relative to the horizontal, the hill slopes 11...

Law Of Sines
A 25 m tower standing vertically on a hillside casts a shadow down the hillside that is 27 m long. The angle at the tip of the shadow S, subtended by the tower is 26. What is the angle of elevation of the sun at S

Law Of Sines
A boat is sailing due east parallel to the shoreline at a speed of 10 miles per hour. At a given time the bearing to the light house is S 70 degrees W and 15 minutes later the bearing is S 63 ...

Domain of a Function
Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation:
C(g)=3.03(g)
a) What does the number 3.03 represent?
b) Find C(2)
c) Find C(9)
d) For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose the number you did.
e) If you were to graph C(g), what would be an appropriate domain? ...

Law Of Sines
to find the distance from the house at A to the house at B, a surveyoor measures the anges BAC to be 40 degrees and then walks off a distance of 100 feet to C and measures the angle ACB to be 50 ...

Law Of Sines
To find the length of the span of a proposed ski lift from A to B, a survey or measures the angle DAB to be 25 degrees and then walks off a distance of 1000ft to C and measures the angles ACB to 15 ...

Undefined Slope
A tank can be filled in 12 minutes by two pipes running simultaneously. By the larger pipe it can be filled in two minutes less time than by the ...

Slope Intercept Form
A store charges a flat fee of $6.75 plus $1.75 for every poung to mail packages. Write an equation in intercept form relating the cost of mailing a package, c, to the number of poins, p, the package ...

Range of a Function
A group of scuba divers are diving in Hawaii at Hanama Bay. The pressure on a
diver at a depth of d feet is given by the formula P = 64d + 2112
where P represents the pressure in pounds per square foot. Amongst the divers
the pressures range from 4032 pounds per square foot to 3552 pounds per
square ...

Slope Intercept Form
a website charges $12 to buy a hat and a shipping charge of $5 per order. find the cost of buying 7 hats

Sine
a ship is sailing toward a small island 800 miles away. if the ship is 2 degrees of course, by how many miles will it miss he island

Slope Intercept Form
below are the graphs of x=-1 and y=7.Find the point at which the two graphs intersect

Zero Slope
Find the slope m of the line that passes through the points (4, 1) and (4, 10) if possible. m=

Slope Intercept Form
jacob has 50 dollars and spends 2.50 on hotdogs everyday for a week how much money does he have after one week

Slope Intercept Form
T(h)=0.8^2-17.6h+93.6 t= temp h=hours since storm began what was the temp as the storm began?
how many hours until the temp dropped below 0
how many hours did the temp remain below 0
coldest temp recorded during the storm
round if necessary

Trigonometric Functions
A mountain peak C is 4130 ft above sea level, and from c the angle of elevation of the second peak B is 5 degree. An aviator at directly over peak c, find angle CAB is 43.8 degree where his altimeter show that he is 8460 ft above sea ...

Slope Intercept Form
To service her car before a trip, Ms. Stein bought motor oil for $1.25 per quart and engine coolant for $2..50 a quart. Altogether she bought 10 quarts and spent $15. How many quarts of motor oil and coolant did ...

Trigonometric Functions
WATER LEVEL IN A HARBOR: the water level (in feet) in Boston Harbor during a certain 24-hr period is approimated by the formula:

H= 4.8sin Pi/6 (t-10) + 7.6 (0 < t < 24)

when t=0 corresponds to 12 am. When is the water level rising and when is falling? Find the relative extrema of H and interpret the results

Trigonometric Functions
At a local airport, a light that produces a powerful white-green beam is placed on the top of a 45-foot tower. If the tower is at one end of the ...

Trigonometric Functions
a 10-ft ladder leans against a wall at an angle with the horizontal.The top of the ladder is x feet above the ground.If the bottom of the ladder is pushed toward the ...

Slope of a Function
Betty's Phone Service has been calling you to join their service to enjoy low rates. With her plan, for 25 minutes of use per month, you pay $7.95. If you use 40 minutes, you monthly charge is $10.35. find the rate of change for this phone ...

Trigonometric Functions
A 50 foot tall tree casts a shadow that is 40 feet long. Draw a picture on your scratch paper, including the "ray of sunshine" causing the shadow. ...

Trigonometric Functions
three times the sine of a certain in angle is twice of the square of the cosine of the same ...

Slope of a Function
Jack follows a 2200 calorie per-day diet. He has 11 servings of bread and cereals, which average 140 calories each. Yesterday, he had a combined 9 servings of fruits and vegetables averaging 60 caloeries ...

Slope of a Function
A plumber charged $110 for a thre-hour job and $160 for a five-hour job. At this ...

Functions
A camera manufacturer spends $2,100 each day for overhead expenses plus $9 per camera for labor and
materials. The cameras sell for $14 each.
a. How many cameras must the company sell in one day to equal its daily costs?
b. If the manufacturer can increase production by 50 cameras per ...

Functions
as the time increases by 0.2 seconds,by how much does the distance ...

Functions
Suppose a population of initial size 100 grows at the rate of 8% per year forever.
What is the size of the population at the end of year 1?
What is the size of the population at the end of year 2?
What is the size of the population at the end of year 3?
What is the size of the population at the end of year n (for any integer n)...

Functions
Find the lines tangent to the curve y= x^3 + x, where the slope is equal to 4...

Functions
Business and finance. Julio works as a quality control expert in a beverage
factory. The assembly line that he monitors produces about 20,000 bottles in a
24-hour period. Julio samples about 120 bottles an hour and rejects the line if
he finds more than of the sample to be ...

Functions
A saleperson receives a base salary of $200 per week and commission of 10% on sales over $3000...

Functions
Wholesales of bottled water in the United States in 2006 were $10.6 billion. This was an increase of about 54% over sales in 2001...

Functions
A ladder leans against a window in a two-story building. The window is 16 feet off the ground. The base of the ladder is 12 feet from the base of the ...